On simples in a cosilting heart and mutation of cosilting pairs

2026/08/05 by Ramin Ebrahimi, Rasool Hafezi, Jiaqun Wei
Mathematics · #math.RT #math.RA

paper · pdf

arxiv created 2026/08/05 · arxiv updated 2026/08/06

Abstract

Let A be a finite dimensional algebra. The lattice of torsion pairs in \rm mod (A) is controlled by cosilting pairs, infinitely generated analogues of support τ^--tilting pairs. Then, edges in the Hasse quiver (i.e. minimal inclusions of torsion-free classes) correspond to irreducible mutations of cosilting pairs. An important difference with classical τ-tilting theory is that not all indecomposable summands of a cosilting pair are mutable. So, it is very important to identify mutable indecomposable summands in a given cosilting pair. It is well-known that mutable summands correspond to injective envelopes of finitely presented simples in the HRS-tilted heart. Based on this correspondence, we first present a method for obtaining all simples in the HRS-tilted heart, and then give some necessary and sufficient conditions for an indecomposable summand of a given cosilting pair to be left mutable or right mutable.

Citations

• Semibrick-cosilting correspondence
• Torsion pairs via the Ziegler spectrum
• Simples in a cotilting heart
• Mutation and torsion pairs
• A brick version of a theorem of Auslander
• Infinity-tilting theory
• Minimal inclusions of torsion classes
• Silting and cosilting classes in derived categories
• Cosilting complexes and AIR-cotilting modules
• Cosilting Modules
• Silting modules